One option for combustion in zero-emission Integrated Gasification Combined Cycle (IGCC) power plants is non-premixed combustion of nitrogen-diluted hydrogen in air. An important aspect to non-premixed combustion is flame stability or anchoring, though only a few fundamental stability studies of these flames have taken place to date. The following paper presents the results of experiments investigating the effects of nitrogen diluent fraction, jet diameter, and exit velocity on the static stability limits of a turbulent hydrogen jet flame issuing from a thin-lipped tube into a quiescent atmosphere. Four different stability limits are observed: detachment from the burner lip, reattachment to the burner lip, transition from a laminar lifted flame base to blowout or to a turbulent lifted flame, and transition from a turbulent lifted flame to blowout. The applicability of existing theories and correlations to the stability results is discussed. These results are an important step in assessing the viability of a non-premixed combustion approach using hydrogen diluted with nitrogen as a fuel.